An algebraic approach to general aggregation theory: Propositional-attitude aggregators as MV-homomorphisms
AbstractThis paper continues Dietrich and List's  work on propositional-attitude aggregation theory, which is a generalised unification of the judgment-aggregation and probabilistic opinion-pooling literatures. We first propose an algebraic framework for an analysis of (many-valued) propositional-attitude aggregation problems. Then we shall show that systematic propositional-attitude aggregators can be viewed as homomorphisms in the category of C.C. Chang's  MV-algebras. Since the 2-element Boolean algebra as well as the real unit interval can be endowed with an MV-algebra structure, we obtain as natural corollaries two famous theorems: Arrow's theorem for judgment aggregation as well as McConway's  characterisation of linear opinion pools.
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Bibliographic InfoPaper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 445.
Length: 12 pages
Date of creation: Mar 2011
Date of revision:
propositional attitude aggregation; judgment aggregation; linear opinion pooling; Arrow's impossibility theorem; many-valued logic; MV-algebra; homomorphism; Arrow's impossibility theorem; functional equation;
Find related papers by JEL classification:
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-03-26 (All new papers)
- NEP-CDM-2011-03-26 (Collective Decision-Making)
- NEP-HPE-2011-03-26 (History & Philosophy of Economics)
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